Last year, around May, DynDNS.com has changed their root certificates, causing Dynamic DNS using DynDNS.com no longer to work properly. The error (Network Error) is displayed immediately after adding the account to your Sonicwall.

The easiest solution is to upgrade to the latest firmware:

For 5.8, this is at least 5.8.4.0;

For 5.9, this is anything after June 2014.

Dell Support also offers an alternative, although this only works with more recent 5.9 versions: